In this paper, we investigate an optimal boundary control problem for a two dimensional simplified Ericksen–Leslie system modelling the incompressible nematic liquid crystal flows. The hydrodynamic system consists of the Navier–Stokes equations for the fluid velocity coupled with a convective Ginzburg–Landau type equation for the averaged molecular orientation. The fluid velocity is assumed to satisfy a no-slip boundary condition, while the molecular orientation is subject to a time-dependent Dirichlet boundary condition that corresponds to the strong anchoring condition for liquid crystals. We first establish the existence of optimal boundary controls. Then we show that the control-to-state operator is Fréchet differentiable between appropriate Banach spaces and derive first-order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables.
Optimal Boundary Control of a Simplified Ericksen–Leslie System for Nematic Liquid Crystal Flows in 2D / C. Cavaterra, E. Rocca, H. Wu. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 224:3(2017), pp. 1037-1086.
Optimal Boundary Control of a Simplified Ericksen–Leslie System for Nematic Liquid Crystal Flows in 2D
C. CavaterraPrimo
;
2017
Abstract
In this paper, we investigate an optimal boundary control problem for a two dimensional simplified Ericksen–Leslie system modelling the incompressible nematic liquid crystal flows. The hydrodynamic system consists of the Navier–Stokes equations for the fluid velocity coupled with a convective Ginzburg–Landau type equation for the averaged molecular orientation. The fluid velocity is assumed to satisfy a no-slip boundary condition, while the molecular orientation is subject to a time-dependent Dirichlet boundary condition that corresponds to the strong anchoring condition for liquid crystals. We first establish the existence of optimal boundary controls. Then we show that the control-to-state operator is Fréchet differentiable between appropriate Banach spaces and derive first-order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables.File | Dimensione | Formato | |
---|---|---|---|
CRW31012017.pdf
accesso aperto
Tipologia:
Post-print, accepted manuscript ecc. (versione accettata dall'editore)
Dimensione
265.08 kB
Formato
Adobe PDF
|
265.08 kB | Adobe PDF | Visualizza/Apri |
art%3A10.1007%2Fs00205-017-1095-2.pdf
accesso aperto
Tipologia:
Publisher's version/PDF
Dimensione
934.76 kB
Formato
Adobe PDF
|
934.76 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.